To elaborate, given an audible, sinusoidal wave $A\sin(ft)$ with constant $A$ and $f$. That sounds constant to us.
Now from a few posts linked below, I understand that as stereocilia of the hair cells at the corresponding region moves, Spiral ganglion cells (SGCs) associated with these hair cells start to fire trains of neural signals with firing rate sinusoidally deviates from silent baseline rate.
Till this point, instead of something similar to power spectrograms, we just more or less have a fake "frequency axis", along with neural signal trains that are still vibration-like. I am guessing one of the following:
Groups of SGCs approximately cover all phases and the sum of their neural signal trains (due to rate coding) ends up with a approximately constant firing rate (and can be used as a amplitude reference)
Rate coding does not really go beyond giving a better vibrating train than individual SGC train. And cochlear nucleus and beyond are doing some hard work to convert the trains into something that sounds constant.
How do hair cells recognize frequencies?
How does the inner ear encode sound intensity?